If you take out the hyphen, yes. It may not be the right word but this is not a question of grammar. Americans tend to use 'one fourth', and British people tend to use 'a quarter', but really it's a matter of personal preference.
Yes, saying "one-fourth" is grammatically correct. It is another way of expressing the fraction "1/4" or "a quarter." Both terms are commonly used and understood in English.
No, the grammatically correct sentence would be: "I am annoyed by the way you behave."
No, the saying "to love is endurance" is not grammatically correct. It should be "to love is to endure" or "love is endurance."
yes
"Try saying three tall trees" is correct.
It can be, like in the following sentence. There were many firsts in this historic week.
Yes. A quarter is a period of time and one might say during the week or during the day, so during the quarter is just as correct.
No, the grammatically correct sentence would be: "I am annoyed by the way you behave."
no
yes
Certainly. If one were to make a comparison saying "He can run as quick as a cheetah" then it would be grammatically correct.
No, the saying "to love is endurance" is not grammatically correct. It should be "to love is to endure" or "love is endurance."
No. Since "circumspect" is an adjective, "I appreciate your circumspect" is about as grammatically correct as "I appreciate your clean". Saying "I appreciate your circumspect behavior" is correct, similar to "I appreciate your clean appearance".
"Try saying three tall trees" is correct.
It can be, like in the following sentence. There were many firsts in this historic week.
No, it is not grammatically correct to say, 'revert back to'. You would simply say 'revert', as in 'Can we revert to the previous subject?' Revert means to go back (to something), so saying 'revert back to' is saying the same thing twice, which is called tautology.
No, the sentence "You are prejudice" is not grammatically correct. Prejudice is a noun, and you is a pronoun. The sentence essentially is saying that "you" are something that you can not possibly be - the noun prejudice. To make the point you're trying to make, you need an adjective to follow the verb "are." Prejudiced is the descriptive adjective form of prejudice, so the grammatically correct sentence should be "You are prejudiced."
Only if punctuated: Thanks, God. If not directly addressing the Almighty, Thank God is the correct form.